We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

The determination of the intersection curve between Bézier Surfaces may be seen as the composition of two separated problems: determining initial points and tracing the intersection curve from these points. The Bézier Surface is represented by a parametric function (polynomial with two variables) that maps a point in the tridimensional space from the bidimensional parametric space. In this article, it is proposed an algorithm to determine the initial points of the intersection curve of Bézier Surfaces, based on the solution of polynomial systems with the Projected Polyhedral Method, followed by a method for tracing the intersection curves (Marching Method with differential equations). In order to allow the use of the Projected Polyhedral Method, the equations of the system must be represented in terms of the Bernstein basis, and towards this goal it is proposed a robust and reliable algorithm to exactly transform a multivariable polynomial in terms of power basis to a polynomial written in terms of Bernstein basis .

Prostacyclin I2 inhibits platelet aggregation through specific binding to its membrane receptor. In this work, we developed 3D-QSAR models for a series of aromatic heterocyclic compounds from literature using the local intersection volume descriptor. The models obtained can be applied to design new PGI2 receptor ligands with potential platelet anti-aggregating activity.

The purpose of this talk is to present an (apparently) new way to look at the intersection complex of a singular variety over a finite field, or, more generally, at the intermediate extension functor on pure perverse sheaves, and an application of this to the cohomology of noncompact Shimura varieties.; Mathematics

Consider a matroid of rank n in which each element has a real-valued cost and one of d > 1 colors. A class of matroid intersection problems is studied in which one of the matroids is a partition matroid that specifies that a base have qj elements of color j, for j = 1, 2, ... , d. Relationships are characterized among the solutions to the family of problems generated when the vector (q1, q2, ... , qd) is allowed to range over all values that sum to n. A fast algorithm is given for solving such matroid intersection problems when d is small. A characterization is presented for how the solution changes when one element changes in cost. Data structures are given for updating the solution on-line each time the cost of an arbitrary matroid element is modified. Efficient update algorithms are given for maintaining a color-constrained minimum spanning tree in either a general or a planar graph. An application of the techniques to finding a minimum spanning tree with several degree-constrained vertices is described.

We propose a more efficient privacy preserving set intersection protocol which improves the previously known result by a factor of O(N) in both the computation and communication complexities (N is the number of parties in the protocol). Our protocol is obtained in the malicious model, in which we assume a probabilistic polynomial-time bounded adversary actively controls a fixed set of t (t < N/2) parties. We use a (t + 1,N)-threshold version of the Boneh-Goh-Nissim (BGN) cryptosystem whose underlying group supports bilinear maps. The BGN cryptosystem is generally used in applications where the plaintext space should be small, because there is still a Discrete Logarithm (DL) problem after the decryption. In our protocol the plaintext space can be as large as bounded by the security parameter τ, and the intractability of DL problem is utilized to protect the private datasets. Based on the bilinear map, we also construct some efficient non-interactive proofs. The security of our protocol can be reduced to the common intractable problems including the random oracle, subgroup decision and discrete logarithm problems. The computation complexity of our protocol is O(NS2τ3) (S is the cardinality of each party's dataset), and the communication complexity is O(NS2τ) bits. A similar work by Kissner et al. (2006) needs O(N2S2τ3) computation complexity and O(N2S2τ) communication complexity for the same level of correctness as ours.; Yingpeng Sang...

The original publication is available at http://www.springerlink.com/content/14jtbl19nh37ggtx/fulltext.pdf; A "chaos expansion" of the intersection local time functional of two independent Brownian motions in Rd is given. The expansion is in terms of normal products of white noise (corresponding to multiple Wiener integrals). As a consequence of the local structure of the normal products, the
kernel functions in the expansion are explicitly given and exhibit clearly the dimension dependent singularities of the local time functional. Their Lp-properties are discussed. An important tool for
deriving the chaos expansion is a computation of the "S-transform" of the corresponding regularized intersection local times and a control about their singular limit.; peerreviewed

Let X be a pseudomanifold. In this text, we use a simplicial blow-up to
define a cochain complex whose cohomology with coefficients in a field, is
isomorphic to the intersection cohomology of X, introduced by M. Goresky and R.
MacPherson.
We do it simplicially in the setting of a filtered version of face sets, also
called simplicial sets without degeneracies, in the sense of C.P. Rourke and
B.J. Sanderson. We define perverse local systems over filtered face sets and
intersection cohomology with coefficients in a perverse local system. In
particular, as announced above when X is a pseudomanifold, we get a perverse
local system of cochains quasi-isomorphic to the intersection cochains of
Goresky and MacPherson, over a field. We show also that these two complexes of
cochains are quasi-isomorphic to a filtered version of Sullivan's differential
forms over the field Q. In a second step, we use these forms to extend
Sullivan's presentation of rational homotopy type to intersection cohomology.
For that, we construct a functor from the category of filtered face sets to a
category of perverse commutative differential graded Q-algebras (cdga's) due to
Hovey. We establish also the existence and unicity of a positively graded,
minimal model of some perverse cdga's...

We apply ideas from intersection theory on toric varieties to tropical
intersection theory. We introduce mixed Minkowski weights on toric varieties
which interpolate between equivariant and ordinary Chow cohomology classes on
complete toric varieties. These objects fit into the framework of tropical
intersection theory developed by Allermann and Rau. Standard facts about
intersection theory on toric varieties are applied to show that the definitions
of tropical intersection product on tropical cycles in $\R^n$ given by
Allermann-Rau and Mikhalkin are equivalent. We introduce an induced tropical
intersection theory on subvarieties on a toric variety. This gives a
conceptional proof that the intersection of tropical $\psi$-classes on
$\cmbar_{0,n}$ used by Kerber and Markwig computes classical intersection
numbers.

Let $B^{\alpha_i}$ be an $(N_i,d)$-fractional Brownian motion with Hurst
index ${\alpha_i}$ ($i=1,2$), and let $B^{\alpha_1}$ and $B^{\alpha_2}$ be
independent. We prove that, if $\frac{N_1}{\alpha_1}+\frac{N_2}{\alpha_2}>d$,
then the intersection local times of $B^{\alpha_1}$ and $B^{\alpha_2}$ exist,
and have a continuous version. We also establish H\"{o}lder conditions for the
intersection local times and determine the Hausdorff and packing dimensions of
the sets of intersection times and intersection points.
One of the main motivations of this paper is from the results of Nualart and
Ortiz-Latorre ({\it J. Theor. Probab.} {\bf 20} (2007)), where the existence of
the intersection local times of two independent $(1,d)$-fractional Brownian
motions with the same Hurst index was studied by using a different method. Our
results show that anisotropy brings subtle differences into the analytic
properties of the intersection local times as well as rich geometric structures
into the sets of intersection times and intersection points.; Comment: 27 pages

We continue the approach toward a purely combinatorial "virtual" intersection
cohomology for possibly non-rational fans, based on our investigation of
equivariant intersection cohomology for toric varieties (see math.AG/9904159).
Fundamental objects of study are "minimal extension sheaves" on "fan spaces".
These are flabby sheaves of graded modules over a sheaf of polynomial rings,
satisfying three relatively simple axioms that characterize the properties of
the equivariant intersection cohomology sheaf on a toric variety, endowed with
the finite topology given by open invariant subsets. These sheaves are models
for the "pure" objects of a "perverse category"; a "Decomposition Theorem" is
shown to hold. -- Formalizing those fans that define "equivariantly formal"
toric varieties (where equivariant and non-equivariant intersection cohomology
determine each other by Kunneth type formulae), we study "quasi-convex" fans
(including fans with convex or with "co-convex" support). For these, there is a
meaningful "virtual intersection cohomology". We characterize quasi-convex fans
by a topological condition on the support of their boundary fan and prove a
generalization of Stanley's "Local-Global" formula realizing the intersection
Poincare polynomial of a complete toric variety in terms of local data. Virtual
intersection cohomology of quasi-convex fans is shown to satify Poincare
duality. To describe the local data in terms of virtual intersection cohomology
of lower-dimensional complete polytopal fans...

Random $s$-intersection graphs have recently received much interest in a wide
range of application areas. Broadly speaking, a random $s$-intersection graph
is constructed by first assigning each vertex a set of items in some random
manner, and then putting an undirected edge between all pairs of vertices that
share at least $s$ items (the graph is called a random intersection graph when
$s=1$). A special case of particular interest is a uniform random
$s$-intersection graph, where each vertex independently selects the same number
of items uniformly at random from a common item pool. Another important case is
a binomial random $s$-intersection graph, where each item from a pool is
independently assigned to each vertex with the same probability. Both models
have found numerous applications thus far including cryptanalysis, and the
modeling of recommender systems, secure sensor networks, online social
networks, trust networks and small-world networks (uniform random
$s$-intersection graphs), as well as clustering analysis, classification, and
the design of integrated circuits (binomial random $s$-intersection graphs).
In this paper, for binomial/uniform random $s$-intersection graphs, we
present results related to $k$-connectivity and minimum vertex degree.
Specifically...

Let $G$ be a group. The intersection graph of subgroups of $G$, denoted by
$\mathscr{I}(G)$, is a graph with all the proper subgroups of $G$ as its
vertices and two distinct vertices in $\mathscr{I}(G)$ are adjacent if and only
if the corresponding subgroups having a non-trivial intersection in $G$. In
this paper, we classify the finite groups whose intersection graph of subgroups
are toroidal or projective-planar. In addition, we classify the finite groups
whose intersection graph of subgroups are one of bipartite, complete bipartite,
tree, star graph, unicyclic, acyclic, cycle, path or totally disconnected. Also
we classify the finite groups whose intersection graph of subgroups does not
contain one of $K_5$, $K_4$, $C_5$, $C_4$, $P_4$, $P_3$, $P_2$, $K_{1,3}$,
$K_{2,3}$ or $K_{1,4}$ as a subgraph. We estimate the girth of the intersection
graph of subgroups of finite groups. Moreover, we characterize some finite
groups by using their intersection graphs. Finally, we obtain the clique cover
number of the intersection graph of subgroups of groups and show that
intersection graph of subgroups of groups are weakly $\alpha$-perfect.; Comment: 38 pages, 10 figures. arXiv admin note: text overlap with
arXiv:1505.03462, some corrections made

This dissertation places intersection homology and local homology within the framework of persistence, which was originally developed for ordinary homology by Edelsbrunner, Letscher, and Zomorodian. The eventual goal, begun but not completed here, is to provide analytical tools for the study of embedded stratified spaces, as well as for high-dimensional and possibly noisy datasets for which the number of degrees of freedom may vary across the parameter space. Specifically, we create a theory of persistent intersection homology for a filtered stratified space and prove several structural theorems about the pair groups asso- ciated to such a filtration. We prove the correctness of a cubic algorithm which computes these pair groups in a simplicial setting. We also define a series of intersec- tion homology elevation functions for an embedded stratified space and characterize their local maxima in dimension one. In addition, we develop a theory of persistence for a multi-scale analogue of the local homology groups of a stratified space at a point. This takes the form of a series of local homology vineyards which allow one to assess the homological structure within a one-parameter family of neighborhoods of the point. Under the assumption of dense sampling...

In CAD/CAM modeling, objects are represented using the Boundary Representation (ANSI Brep) model Detection of possible intersection between objects can be based on the objects' boundaries (ie., triangulated surfaces), and computed using triangle-triangle intersection. Usually only a cross intersection algorithm is needed; however, it is beneficial to have a single robust and fast intersection detection algorithm for both cross and coplanar intersections. For qualitative spatial reasoning, a general-purpose algorithm is desirable for accurately differentiating the relations in a region connection calculus, a task that requires consideration of intersection between objects. Herein we present a complete uniform integrated algorithm for both cross and coplanar intersection. Additionally, we present parametric methods for classifying and computing intersection points. This work is applicable to most region connection calculi, particularly VRCC-3D+, which detects intersections between 3D objects as well as their projections in 2D that are essential for occlusion detection.

A fuzzy sets intersection procedure to select the optimum sizes of analog circuits composed of metal-oxide-semiconductor field-effect-transistors (MOSFETs), is presented. The cases of study are voltage followers (VFs) and a current-feedback operational amplifier (CFOA), where the width (W) and length (L) of the MOSFETs are selected from the space of feasible solutions computed by swarm or evolutionary algorithms. The evaluation of three objectives, namely: gain, bandwidth and power consumption; is performed using HSPICE™ with standard integrated circuit (IC) technology of 0.35um for the VFs and 180nm for the CFOA. Therefore, the intersection procedure among three fuzzy sets representing "gain close to unity", "high bandwidth" and "minimum power consumption", is presented. The main advantage relies on its usefulness to select feasible W/L sizes automatically but by considering deviation percentages from the desired target specifications. Basically, assigning a threshold to each fuzzy set does it. As a result, the proposed approach selects the best feasible sizes solutions to guarantee and to enhance the performances of the ICs in analog signal processing applications.

With the increasing demand on today's roadway systems, intersections are beginning to fail at alarming rates prior to the end of their design periods. Therefore, maintaining safety and operational efficiency at intersections on arterial roadways remains a constant goal. This effort for sustainability has spawned the creation and evaluation of numerous types of unconventional intersection designs. Several unconventional designs exist and have been studied, including the Bowtie, Continuous Flow Intersection, Paired Intersection, Jughandle, Median U-Turn, Single Quadrant Roadway and Superstreet Median. Typically, these designs eliminate/reroute conflicting left-turn manoeuvres to and from the minor or collector cross road. High left-turning volumes are addressed by adding an exclusive left-turning signal. This consequently increases the required number of signal phases and shorter green time for the major through traffic. This paper describes the evaluation of an unconventional intersection designed to lessen the effects of high left-turning traffic. To aid in the evaluation of the unconventional Superstreet design, a comparison of a Conventional intersection's operation was made. Constructing and analysing a live Superstreet and Conventional intersection design is a massive undertaking. Microscopic traffic models were developed and tested using CORSIM. A variety of scenarios were created by changing the approach volumes and turning percentages on the major/minor roads to reflect different congestion levels that may occur at the intersection on any given day. The total number of created scenarios was 72...